A Linear Unconditionally Stable Scheme for the Incompressible Cahn–Hilliard–Navier–Stokes Phase-Field Model

2021 ◽  
Author(s):  
Xue Wang ◽  
Kaitai Li ◽  
Hongen Jia
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Navier Stokes ◽  
Unconditionally Stable ◽  
Stable Scheme

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

2014 ◽  
Vol 24 (09) ◽  
pp. 1450110 ◽  
Author(s):  
Rodica Borcia ◽  
Michael Bestehorn
Keyword(s):  
Liquid Film ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Bottom Plate ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations ◽  
Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

scholarly journals Experimental and numerical modeling for flattening and rapid solidification with crystallization behavior of supersonic ceramic droplets

2020 ◽  
Author(s):  
Y. Wang ◽  
Y Bai ◽  
K Wu ◽  
J Zhou ◽  
M G Shen ◽  
...  
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Crystallization Behavior ◽  
Field Model ◽  
Solidification Rate ◽  
Phase Field Model ◽  
Oriented Attachment ◽  
Navier Stokes ◽  
Columnar Grains ◽  
And Migration

Abstract Successive impingement of supersonic droplets after refining in plasma jet usually forms a fine-lamellar structured coating with high mechanical properties. However, the comprehensive process (such as flattening, rapid solidification and crystallization) of high-velocity impact of refined droplets is difficult to understand. In this study, an experimental study showed that the content of refinement droplets reached to 90 % and displayed the multi-scale equiaxed grains morphology at extremely rapid solidification rate. Phase-field model revealed a hybrid coalescence growth of oriented attachment and migration of grains boundary under the dynamic temperature gradient. Furthermore, an optimized numerical model that consisted of the Navier-Stokes and energy balance equations coupled with the Cahn-Hilliard and phase-field model for growth orientation of grains was developed to accurately reproduce the comprehensive process of refined supersonic droplets. The size distribution and crystallographic orientation of columnar grains for single or two flattened droplets were in a good agreement with the experimental results. The interface between two-flattened droplets exhibited an epitaxial growth of columnar grains. This optimized model can be an effective method in predicting the flattening and solidification with crystallization behavior of droplets during plasma spraying.

Sign in / Sign up

Export Citation Format

Share Document